Remember that the Bennets and Gardiners wanted to hush up the fact that there was such a long delay between the elopement and the wedding. Although the Gardiners did their best to give Lydia a proper (though tiny) wedding, I'm sure they would *not* want her to be married in their own church, where the rest of the congregation would probably know them well, and start asking questions if they heard that the Gardiners' niece had been married there! As I said in a previous post, if it became generally known that their eloped-but-still-unmarried niece had stayed with the Gardiners *before* her wedding, IMO *their* reputation would suffer too (which is part of the reason why the (sensible members of) the Bennet family were so grateful to the Gardiners).

Though St. Clement's might be Wickham's official parish, I don't think anybody would recognize him there, since I doubt very much that he ever darkened that particular church door during his time(s?) in London! (I picture him simply having to hand over the equivalent of his hydro or phone bill to prove that he actually lived in the parish, and the clergyman starting to fill out the necessary paperwork!)

Also, I suspect that it might have been less complicated (legally speaking) for Lydia and Wickham to be married in a church that one of them officially belonged to, but somebody else can probably answer this better than I can. Thanks for pointing this out about St. Clement's - despite all the times I've read the book, I have the scene from P&P2 in my head, which sort of makes it look like the Wickhams were married at the Gardiners' church!